![]() ![]() Time steps are sometimes called ‘generations’. The initial state of the game is the ‘seed’ and all cells are updated simultaneously. Rule 1 represents ‘death by under-population’ rule 2 represents ‘sustainable life’ rule 3 represents ‘death by over-population’, and rule 4 represents ‘birth’. These rules can be thought to represent basic processes of life and death, motivating the name ‘Game of Life’. And ‘off’ cell (t -1) with exactly three ‘on’ neighbours (t -1) transitions to an ‘on’ state at time t.Any ‘on’ cell (t -1) with more than three ‘on’ neighbours (t -1) transitions to an ‘off’ state at time t.Any ‘on’ cell (t -1) with two or three ‘on’ neighbours (t -1) remains ‘on’ at time t.Any ‘on’ cell (at time t-1) with fewer than two ‘on’ neighbours (at t -1) transitions to an ‘off’ state at time t.The game takes place in discrete time, with the state of each cell at time t determined by its own state and the states of its eight immediate neighbours at t-1 (the Moore neighbourhood of radius 1), according to the following simple rules: In its standard format, the Game of Life unfolds on an infinite two-dimensional grid composed of cells each of which is either ‘on/alive’ or ‘off/dead’. 5 Implications: Emergence, self-organization, autopoeisis, and the physics of information. ![]() Even though its (simple) rules are specified at the level of individual cells, one sees entities at coarse-grained ‘higher’ levels of description, whose behaviors are better described by rules at these higher levels. One reason for its appeal is that it is very simple to program, yet at the same time it appears to exemplify emergent and self-organized behaviour. First popularized in 1970 in the Scientific American (Gardner, 1970), the Game of Life has attracted lasting appeal among both scientific and amateur communities. Following specification of an initial configuration, patterns evolve over time across the grid requiring no further user input (thus ‘zero-player’). It takes place on an infinite two-dimensional grid in which cells can be ‘on’ (alive) or ‘off’ (dead), and is defined by a set of rules that jointly determine the state of a cell given the state of its neighbours. The Game of Life (sometimes known simply as Life) is an example of a cellular automaton and a zero-player game. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopediaĭr. FuncAnimation ( fig, animate, init_func = init, frames = frames, interval = interval ) #print anim_to_html(anim) return display_animation ( anim, default_mode = mode ) This is called sequentially def animate ( i ): im. set_data ( X_blank ) return ( im ,) # animation function. set_clim ( - 0.05, 1 ) # Make background gray # initialization function: plot the background of each frame def init (): im. add_axes (, xticks =, yticks =, frameon = False ) im = ax. figure ( figsize = figsize, dpi = dpi ) ax = fig. This controls the size of the game board on the screen frames : integer The number of frames to compute for the animation interval : float The time interval (in milliseconds) between frames mode : string The default mode of the animation. # JSAnimation import available at from JSAnimation.IPython_display import display_animation, anim_to_html from matplotlib import animation def life_animation ( X, dpi = 10, frames = 10, interval = 300, mode = 'loop' ): """Produce a Game of Life Animation Parameters - X : array_like a two-dimensional numpy array showing the game board dpi : integer the number of dots per inch in the resulting animation. ![]()
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